4570 Inorg. Chem. 2010, 49, 4570–4577 DOI: 10.1021/ic100118q
M3(Au,Ge)19 and M3.25(Au,Ge)18 (M = Ca, Yb): Distinctive Phase Separations Driven by Configurational Disorder in Cubic YCd6-Type Derivatives Qisheng Lin and John D. Corbett* Department of Chemistry, Iowa State University, Ames, Iowa 50010 Received January 19, 2010
Exploratory syntheses in the M-Au-Ge (M = Ca, Yb) systems have led to the discovery of two cleanly separated nonstoichiometric phases M3Au∼14.4Ge∼4.6 (I) and M3.25Au∼12.7Ge∼5.3 (II). Single crystal X-ray studies reveal that both (space group Im3) feature body-centered-cubic packing of five-shell multiply endohedral clusters that resemble those in the parent YCd6 (= Y3Cd18) and are akin to approximate phases in other quasicrystal systems. However, differences resulting from various disorders in these are distinctive. The innermost cluster in the M3Au∼14.4Ge∼4.6 phase (I) remains a disordered tetrahedron, as in the YCd6 parent. In contrast, its counterpart in the electron-richer M3.25Au∼12.7Ge∼5.3 phase (II) is a “rattling” M atom. The structural differentiations between I and II exhibit strong correlations between lattice parameters, cluster sizes, particular site occupancies, and valence electron counts.
Quasiperiodic crystals (QCs), or quasicrystals in short, exhibit potential applications in advanced technological materials, for example, surface coatings,2 catalysts,3 thermoelectrics,4 hydrogen storage,5 photonic crystals,6 and bioinspired materials.7 Recently, exploratory syntheses of these unusual materials have aroused the interest of a few chemists.8-12 However, knowledge of QC structures still lag much behind because classic crystallography cannot handle crystal structures with quasiperiodicity,1 which exhibit self-similarity upon inflation/deflation on τ (the golden mean, 1.618) and lack translational periodicity. In particular, an icosahedral QC (i-QC) has quasiperiodicity in three-dimensions, requiring six-dimensional crystallography to fully characterize its structure. Thus, the so-called crystalline approximant (AC) neighbors play important roles in modeling QC structures and in rationalizing the structure-property relationships of QCs. ACs are conventional crystals, and they are assumed to contain local atomic clusters similar to those found in
corresponding QC. In addition, the structure and bonding analyses of various ACs provide an ideal playground for chemists to probe relationships among polar intermetallics, Hume-Rothery, and Zintl phases. In the past 10 years, YCd6-type13 compounds have received renewed interest10,11,14-19 because the isostructural CaCd6 and YbCd6 were found to be 1/1 ACs20 of their QCs, CaCd5.67 and YbCd5.67,21,22 respectively. The building blocks of YCd6type structures are five-shell multiply endohedral clusters, each one of which is ordered from the center out as a disordered tetrahedron (4 atoms total), a pentagonal dodecahedron (20), an icosahedron (12), an icosidodecahedron (30), and an outermost triacontahedron (32 þ 60). However, recent studies have revealed that various disorders may exist in YCd6-type structures.10,11,14,16-19 Particularly, they may contain orientation disorder of the innermost tetrahedron, deformation or disorder of the dodecahedron (including split positions), and occupation of an additional special Wyckoff 8c site (1/4, 1/4, 1/4). (Strictly speaking, occupation at the last position results in a
*To whom correspondence should be addressed. E-mail: jcorbett@ iastate.edu. (1) Janot, C. Quasicrystals: A Primer, 2nd ed.; Oxford University Press: Oxford, U.K., 1994. (2) Rivier, N. J. Non-Cryst. Solids 1993, 153-154, 458. (3) Kameoka, S.; Tanabe, T.; Tsai, A. P. Catal. Today 2004, 93-95, 23. (4) Macia, E. Appl. Phys. Lett. 2000, 77, 3045. (5) Kelton, K. F.; Gibbons, P. C. MRS Bull. 1997, 22, 71. (6) Freedman, B.; Bartal, G.; Segev, M; Lifshitz, R.; Christodoulides, D. N.; Fleischer, J. W. Nature 2006, 446, 1166. (7) Andersen, B. C.; Bloom, P. D.; Baikerikar, K. G.; Sheares, V. V.; Mallapragada, S. K. Biomaterials 2002, 23, 1761. (8) Conrad, M.; Harbrecht, B. Chem.;Eur. J. 2002, 8, 3093. (9) Tsai, A. P. Acc. Chem. Res. 2003, 36, 31. (10) Pay Gomez, C.; Lidin, S. Phys. Rev. B 2003, 68, 024203. (11) Piao, S.; Gomez, C. P.; Lidin, S. Z. Naturforsch. 2006, 61b, 644. (12) Lin, Q.; Corbett, J. D. Struct. Bonding (Berlin) 2009, 133, 1.
(13) Larson, A. C.; Cromer, D. T. Acta Crystallogr. 1971, 27B, 1875. (14) Lin, Q.; Corbett, J. D. Inorg. Chem. 2004, 43, 1912. (15) Ishimasa, T.; Kaneko, Y.; Kaneko, H. J. Non-Cryst. Solids 2004, 334&335, 1. (16) Lin, Q.; Corbett, J. D. J. Am. Chem. Soc. 2005, 127, 12786. (17) Lin, Q.; Corbett, J. D. J. Am. Chem. Soc. 2006, 128, 13268. (18) Lin, Q.; Corbett, J. D. J. Am. Chem. Soc. 2007, 129, 6789. (19) Lin, Q.; Corbett, J. D. Inorg. Chem. 2008, 47, 7651. (20) 1/1 AC denotes an order of the cubic AC. According to high dimensional crystallography, the cell parameters of a q/p cubic AC (aq/p) is related to the QC lattice constant (a6, indexed in six dimensions) by aq/p = 2a6(p þ qτ)/(2 þ τ)1/2, in which τ is the golden mean, and p and q are two consecutive Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, ...)1. (21) Tsai, A. P.; Guo, J. Q.; Abe, E.; Takakura, H.; Sato, T. J. Nature 2000, 408, 537. (22) Takakura, H.; Pay Gomez, C.; Yamamoto, Y.; De Boissieu, M.; Tsai, A. P. Nat. Mater. 2007, 6, 58.
Introduction 1
pubs.acs.org/IC
Published on Web 04/14/2010
r 2010 American Chemical Society
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Table 1. Some Reaction Compositions, Products, and Refined Lattice Constants for YCd6-Type Phases in the M-Au-Ge (M = Ca and Yb) Systems lattice constantsc code
proportion (%)
conditionsa
products and estimated yieldsb
powder data
14.7620(5), 14.6805(5) 14.7669(5),14.6801(5) 14.7676(5), 14.8305(5) 14.7053(5) 14.6838(5) 14.6760(5) 14.8200(5) 14.8063(5) 14.8051(5) 14.6904(5)
14.766(1)
14.6810(5)
14.682(1)
14.6288(5) 14.7678(5), 14.6278(5) 14.7675(5), 14.6692(5) 14.7663(5), 14.6235(5)
14.6334(9) 14.769(2)
single crystal data
crystals
Ca/Au/Ge 1 2 3 4 5 6 7 8 9 10
14.3/64.3/21.4 14.4/62.5/23.1 14.3/60.7/25.0 14.2/59.1/26.7 14.3/57.1/28.6 14.3/50.0/35.7 10.0/65.0/25.0 10.0/60.0/30.0 10.0/50.0/40.0 20.0/55.0/25.0
940/500 900/500 850/400 850/500 850/500 940/500 850/400 850/400 850/400 850/400
11
20.0/50.0/30.0
850/400
75% YCt þ 20% YCsþ U1 70% YCt þ 30% YCs 70% YCs þ 30% YCt >98% YCs >98% % YCs 55% YCsþ 15% CaAu2Ge2 þ30% Ge >98% YCt 60% YCt þ 35% Ge þ U2 50% YCtþ 40% Ge þ U2 20% YCs þ 10% CaAu3Geþ 60% Ca3(Au,Ge)11þ 10% CaAuGe 15% YCsþ 70% Ca3(Au,Ge)11 þ 15% CaAuGe
900/500 900/500 900/500 900/500
55% YCs þ 45% U3 70% YCt þ 30% YCs 55% YCt þ 45% YCs 40% YCt þ 60% YCs
14.764(5), 14.8315(9) 14.712(1) 14.6843(9) 14.670(1) 14.822(1) 14.805(1) 14.807(2)
3, 5 2 s1 1 s2 4
Yb/Au/Ge 12 13 14 15
14.3/50.0/35.7 10.0/65.0/35.0 14.5/62.0/23.5 15.3/58.9/25.9
s3 s4
a The heating and annealing temperatures (°C) are listed. The ramp speed and duration time are same for all reactions, as in the text. b The percentages were estimated according to observed peak intensities in powder patterns. YCs and YCt denote YCd6-type derivatives that are centered by a single atom (II) and a tetrahedron (I), respectively. Ui (i = 1, 2, 3) denote different unknown phases. c Lattice parameters from powder data were refined from five to nine of the strongest peaks within 20°-70°, if discernible, whereas single crystal data were refined from all observed reflections [I > 2σ(I)]. Bold numbers representing lattice parameters for single crystal structures are reported in the text and coded in the last column.
change of structural type, but for convenience these may still be considered as YCd6-type derivatives.) These disorders are not separate phenomena; rather, they exhibit strong correlations. A comprehensive study on MCd6 (M = rare-earth metal) by Lidin and co-workers11 revealed that the orientation of the tetrahedron strongly depends on the size of the M metal. A large M expands the polyhedral shells and results in a remarkable diversity of disorders around the tetrahedron as well as occupation of the additional 8c sites. Further, they showed that the presence of atoms at 8c sites correlates with the deformation of the neighboring dodecahedron and the orientation of the innermost tetrahedron as well. Recently, Fornasini and co-workers23 reported another apparent disorder type, that the building blocks in YbZn5.86 and Yb(Zn,Al)5.75 include both a fractional single Yb atom and a disordered tetrahedron within the dodecahedral shell, a rare case. During continued development of QC systems, we have discovered 1/0, 1/1, and 2/1 ACs and i-QC phases in the Ca-Au-Ga system.19,24 The valence electron count per atom in the Ca15.2(5)Au50.2(6)Ga34.5(4) i-QC (e/a = 1.84) is notably lower than usual (∼2.0), suggesting that substitution of Ga by electron-richer elements (e.g., Ge or Sn) might be a promising electronic way to tune i-QCs and ACs. Moreover, explorations of Ca-Au-Ge/Sn systems might illustrate whether low lying d orbitals on the electropositive element differentiate the formation of YCd613 and Mg32(Al,Zn)4925 type AC structures, noting that both Na52Au80Ge30 and Na60Au78Sn2426 are isostructural with the latter AC structure. Recently, we (23) Fornasini, M. L.; Manfrinetti, P.; Mazzone, D.; Dhar, S. K. Z. Naturforsch. 2008, 63b, 237. (24) Lin, Q.; Corbett, J. D. Inorg. Chem. 2008, 47, 3462. (25) Bergman, G.; Waugh, J. L. T.; Pauling, L. Acta Crystallogr. 1957, 10, 254. (26) Doering, W.; Seelentag, W.; Buchholz, W.; Schuster, H. U. Z. Naturforsch. 1979, 34b, 1715.
also reported the syntheses and structures of two La3Al11 type Ca3Au11-xGex phases (Imm2: ∼ 7.0 < x < 7.5; Pnnm: 7.5 < x < ∼8.0)27 that are neighbors of the present Ca3(Au,Ge)19 and Ca3.25(Au,Ge)18. In this work, we report the syntheses and structures of two distinctively different YCd6-type derivatives in the M-Au-Ge (M = Ca, Yb) systems: One contains a disordered tetrahedron and the other, only a fractional single M atom, as the innermost units in the multiply endohedral clusters. The appearance of both derivatives in a same system is the main novelty. The two phases show pronounced distinctions regarding lattice parameters, compositions, disorders, and valence electron counts. Parallel explorations of the M-Au-Sn (M = Ca, Yb) systems yield very different results, which will be reported separately.28 Experimental Section Synthesis. High purity elements as Ca chunks, Yb particles, Au sheets, and Ge particles (all >99.99%, Alfa-Aesar) were weighed in a N2-filled glovebox (H2O < 0.1 ppm vol.) and weldsealed under Ar into Ta containers. The last were in turn enclosed in evacuated SiO2 jackets ( 2σ(I)] [all data] res. peaks (e A˚-3)a
Ca3.25Au12.50Ge5.50 1.93 2991.59 Im3, 8 14.670(1) 3157.4(4)/12.59 126.95 9936/0.0675 727/0/42 1.177 0.0229/0.0449 0.0270/0.0458 2.124/-2.255
Ca3.25Au12.94(3)Ge5.06(2) 1.87 3046.16 Im3, 8 14.712(1) 3184.3(4)/12.71 129.09 10106/0.0549 727/0/45 1.117 0.0355/0.0902 0.0412/0.0931 4.152/-3.351
Ca3.05(2)Au13.69(8)Ge5.31(6) 1.86 3201.26 Im3, 8 14.764(5) 3217.9(17)/13.23 134.98 14192/0.1930 743/0/51 1.061 0.0575/0.0933 0.0962/0.1023 5.322/-4.309
Ca3Au14.26(6)Ge4.74(5) 1.78 3273.5 Im3, 8 14.805(1) 3244.8(5)/13.40 137.93 10707/0.0679 743/0/51 1.129 0.0354/0.0729 0.0437/0.0758 5.634/-4.256
Ca3Au14.52(6)Ge4.48(5) 1.75 3304.93 Im3, 8 14.8315(9) 3262.5(3)/13.46 138.99 10116/0.0652 747/0/51 1.187 0.0398/0.0917 0.0444/0.0941 5.785/-3.462
a
The largest residual peaks are all around 0.7-1.4 A˚ from Au atoms.
analyses. Four parallel reactions with Yb replacing Ca were also carried out to resolve the uncertainty of assigning Ca or Ge to the special 2a site (below). Table 1 summarizes the loaded proportions, reaction conditions, phase identities, and refined lattice parameters from both powder patterns and single crystals. All products are metallic in appearance, brittle, and evidently inert to moisture and air at room temperature. X-ray Powder Diffraction. Phase analyses were made on the basis of powder diffraction data collected on a Huber 670 Guinier powder camera equipped with an area detector and Cu KR1 radiation (λ = 1.540598 A˚). The detection limit of a minor phase with this instrument and system is conservatively estimated to be about 5 vol % in equivalent scattering power. Therefore, a seemingly pure product is denoted with at least a 95% yield. Phase identification was done with the aid of PowderCell,29 and lattice parameter refinements were performed using UnitCell.30 The lattice parameters refined from powder data were used with single crystal refinement results for bond distance calculations. Single-Crystal X-ray Diffraction. Single crystals were mounted on a Bruker APEX CCD single crystal diffractometer equipped with graphite-monochromatized Mo KR (λ = 0.71069 A˚) radiation. Room temperature intensity data were collected in an ω scan method over 2 θ = ∼ 3-57° range and with exposures of 10-30 s per frame. Data integration, Lorentz polarization, empirical absorption, and other corrections were made by SAINT and SADABS subprograms included in the SMART software package.31 Full-matrix least-squares refinements on Fo2 were performed with the aid of the SHELXTL v 6.1 program.32 Seven Ca- and two Yb-based crystals were structurally characterized in this work. However, results for only five Ca crystals (1-5) are reported in the text as representative, whereas structural data for two more Ca- (s1 and s2) and the two Yb-containing phases (s3 and s4) are given in the Supporting Information. All positional data were standardized by program STRUCTURE TIDY33 and sorted to aid comparisons. The crystallographic, data collection, and structure refinement parameters for 1- 5 are given in Table 2, and the refined positional and isotropic-equivalent displacement parameters are in Table 3. The remaining crystallographic data (cif) are available in the Supporting Information. Direct methods were used to set up initial structural models, generally with eight independent sites. Two other weakly scattering Au/Ge8 and Au32 split sites (Table 3) were located on the basis of (29) Roisnel, T.; Rodrı´ guez-Carvajal, J. WinPLOTR: a Windows tool for powder diffraction patterns analysis. In Materials Science Forum, Proceedings of the Seventh European Powder Diffraction Conference (EPDIC 7), Barcelona, Spain, May 20-23, 2000; Delhez, R., Mittenmeijer, E. J., Eds.; 2000; pp 118-123. (30) Holland, T. J. B.; Redfer, S. A. T. Miner. Mag. 1997, 61, 65. (31) SMART; Bruker AXS, Inc., Madison, WI, 1996. (32) SHELXTL; Bruker AXS, Inc, Madison, WI., 2000. (33) Gelato, L. M.; Parthe, E. J. Appl. Crystallogr. 1987, 20, 139.
difference Fourier maps. The assignment of only a Ca atom to a Wyckoff 2a site in the center of the dodecahedra in crystals 1, 2, 3, s1, and s3 should be noted. The solution of structure 1 is described as an example. The Wyckoff 2a (0, 0, 0) site in 1 could be assigned to either Ca or Ge, with refined occupancies of 0.92 (4) or 0.53 (2), respectively. These yielded two slightly different compositions, Ca3.23(1)Au12.5Ge5.5 or Ca3Au12.5Ge5.633(5), in which the overall atomic percentages varied by only ∼1.1% in Ca or 0.07% in Ge for the two extremes. According to experience, such small variations are about the same level as uncertainties for general EDS instruments. Therefore, no EDS data were collected with the aim to differentiate Ca or Ge for this purpose. Rather, the uncertainty was resolved by the structural solution for crystal s3, Yb3.25Au12.5Ge5.39(3), in which the atom on the 2a site could be unambiguously assigned to pure Yb. Therefore, Ca was also assigned to 2a site in crystals 2, 3, s1, and s3. From the viewpoint of surroundings, Ca fits in those dodecahedra better than Ge as far as the center-to-vertex distance, ∼ 3.6 A˚. In addition, assignment of electropositive metal atoms to the 2a site was previously reported for Yb25.05(3)Zn146.83(9) (= Yb3.18Zn18.35) and Yb25.39(2)Zn138.2(3)Al7.7(3) (= Yb3.24Zn17.28Al0.96).23 Electronic Structure Calculations. The crystallographic data for crystal 1 were input directly as a model of the Ca3.25(Au,Ge)18 phase. However, the model of the Ca3(Au,Ge)19 phase required some modification because straightforward linear-muffin-tin-orbital (LMTO) calculations can only handle disorder-free structural models. Therefore, the structure of crystal 4 was simplified as follows: atoms in the sequence 1 to 4 were assumed being fully occupied by Au1 to Au4, and in the sequence 5-8 by Ge5-Ge8. Moreover, the minor split site (Au32) was omitted. As before,16,18,19,34 subspace group I23 was used to circumvent the problem arising because of the disordered tetrahedron. All of these approximations resulted in a Ca3Au12.5Ge6.5 model. The e/a (2.02) for this model is much larger than in the real crystal 4 though (1.78). Calculations were performed by means of the self-consistent, tight-binding, LMTO method in the local density (LDA) and atomic sphere (ASA) approximations, within the framework of the DFT method.35-38 The ASA radii of Ca, Au, and Ge were automatically scaled to 3.74, 3.00, and 2.75 A˚ (as average values) using the limitation of 18% maximum overlap between neighboring ASA spheres. One independent empty sphere was introduced to the (34) Ishii, Y.; Fujiwara, T. Phys. Rev. Lett. 2001, 87, 206408. (35) Tank, R.; Jepsen, O.; Burkhardt, A.; Andersen, O. K. TB-LMTOASA Program, Vers. 4.7; Max-Planck-Institut f€ur Festk€orperforschung: Stuttgart, Germany, 1994. (36) Shriver, H. L. The LMTO Method; Springer-Verlag: Berlin, Germany, 1984. (37) Jepsen, O.; Snob, M. Linearized Band Structure Methods in Electronic Band-Structure and its Applications, Springer Lecture Notes; Springer Verlag: Berlin, Germany, 1987. (38) Andersen, O. K.; Jepsen, O. Phys. Rev. Lett. 1984, 53, 2571.
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Table 3. Atomic Coordinates and Isotropic Equivalent Displacement Parameters for Ca3.25(Au,Ge)18 (1 and 2), Ca3.05(2)Au13.67(8)Ge5.33(6) (3), and Ca3(Au,Ge)19 (4 and 5) atoma
Wyck.
occ.
x
y
z
Ueq
0.3368(1) 0.4027(1) x 0 0.2302(1) 0 1/4 0 0.1888(2)
0.1965(1) 0.3548(1) x 0 0.0866(1) 1/2 1/4 0 0.3060(2)
0.014(1) 0.010(1) 0.013(1) 0.016(1) 0.011(1) 0.012(1) 0.019(1) 0.047(3) 0.009(1)
0.3376(1) 0.4026(1) x x 0 0.2317(2) 0 1/4 0 0.1881(3)
0.1980(1) 0.3554(1) x x 0 0.0844(1) 1/2 1/4 0 0.3055(3)
0.026(1) 0.020(1) 0.030(1) 0.030(1) 0.027(1) 0.027(1) 0.018(1) 0.040(2) 0.082(10) 0.019(1)
0.3389(1) 0.4024(1) x x 0 0.2378(2) 0 1/4 0.068(2) 0 0.1870(5)
0.2005(1) 0.3561(1) x x 0 0.0845(2) 1/2 1/4 0.071(2) 0 0.3057(5)
0.023(1) 0.017(1) 0.032(1) 0.032(1) 0.025(1) 0.026(1) 0.018(1) 0.046(3) 0.098(10) 0.017b 0.017(2)
0.3400(1) 0.4023(1) x x 0 0.2374(1) 0 1/4 0.0799(6) 0.1857(3)
0.2019(1) 0.3570(1) x x 0 0.0834(1) 1/2 1/4 0.0680(6) 0.3047(3)
0.014(1) 0.008(1) 0.030(1) 0.030(1) 0.015(1) 0.016(1) 0.010(1) 0.045(2) 0.065(3) 0.008(1)
0.3406(1) 0.4023(1) x x 0 0.2364(1) 0 1/4 0.0862(4) 0.1856(3)
0.2021(1) 0.3575(1) x x 0 0.0825(1) 1/2 1/4 0.0669(4) 0.3040(3)
0.028(1) 0.022(1) 0.049(1) 0.049(1) 0.028(1) 0.031(1) 0.021(1) 0.072(2) 0.054(2) 0.022(1)
Ca3.25Au12.50Ge5.50 (1) Au1 Au2 Au3 Au4 Ge5 Ge6 Ge7 Ca8 Ca9
48 h 24 g 16f 12d 24 g 12e 8c 2a 24 g
1 1 1 1 1 1 1 1 1
0.1037(1) 0 0.1420(1) 0.4003(1) 0 0.1989(1) 1/4 0 0 Ca3.25Au12.94(4)Ge5.06(2) (2)
Au1 Au2 Au31 Au32 Au4 Au/Ge5 Ge6 Ge7 Ca8 Ca9
48 h 24 g 16f 16f 12d 24 g 12e 8c 2a 24 g
1 1 0.956(3) 0.044(3) 1 0.145/0.855(8) 1 1 1 1
0.1040(1) 0 0.1427(1) 0.188(1) 0.4013(1) 0 0.1997(2) 1/4 0 0 Ca3.05(2)Au13.69(8)Ge5.31(6) (3)
Au1 Au2 Au31 Au32 Au4 Au/Ge5 Ge6 Ge7 Au/Ge8a Ca8b Ca9
48 h 24 g 16f 16f 12d 24 g 12e 8c 24 g 2a 24 g
1 1 0.968(5) 0.032(5) 1 0.34/0.66(1) 1 1 0.05/0.28(1) 0.22(7) 1
0.1043(1) 0 0.1468(1) 0.1896(6) 4040(2) 0 0.2001(4) 1/4 0 0 0 Ca3Au14.26(6)Ge4.74(5) (4)
Au1 Au2 Au31 Au32 Au4 Au/Ge5 Ge6 Ge7 Au/Ge8 Ca9
48 h 24 g 16f 16f 12d 24 g 12e 8c 24 g 24 g
1 1 0.921(3) 0.079(3) 1 0.435/0.565(8) 1 1 0.153/0.181(9) 1
Au1 Au2 Au31 Au32 Au4 Au/Ge5 Ge6 Ge7 Au/Ge8 Ca9
48 h 24 g 16f 16f 12d 24 g 12e 8c 24 g 24 g
1 1 0.905(4) 0.095(4) 1 0.485/0.515(9) 1 1 0.187/0.147(9) 1
0.1040(1) 0 0.1497(1) 0.0956(7) 0.4047(1) 0 0.2016(2) 1/4 0 0 Ca3Au14.52(6)Ge4.48(5) (5) 0.1038(1) 0 0.1524(1) 0.0920(7) 0.4048(1) 0 0.2020(2) 1/4 0 0
a For comparison, atoms in different structures are sorted in the same order and each independent atom is named in a sequence number for all sites rather than of that for each atom type. b Isotropic displacement parameter was fixed at the value for Ca9 because of its large correlation with occupancy.
Ca3(Au,Ge)19 model and none for Ca3.25(Au,Ge)18. Reciprocal space integrations were carried out by means of the tetrahedron method. Down-folding39 techniques for outer Ca 4p, Au 5f, and Ge 4d orbitals were applied. Scalar relativistic corrections were automatically (39) Lambrecht, W. R. L.; Andersen, O. K. Phys. Rev. B 1986, 34, 2439.
included in the calculations. The band structure was sampled for 24 24 24 k points in the irreducible wedge of the Brillouin zone.
Results and Discussion Partial Ca-Au-Ge Phase Diagram. Currently six ternary phases have been reported in the Ca-Au-Ge
4574 Inorganic Chemistry, Vol. 49, No. 10, 2010
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Figure 1. Partial Ca-Au-Ge phase diagram section at 400-500 °C showing relative phase regions. Blue and red ellipses mark the new phases I and II. Small black dots represent the samples investigated, as numbered in Table 1.
system, CaAuGe (C2/m), CaAuGe (Pnma), CaAu1.24Ge0.76 (Imm2),40 CaAu2Ge2 (I4/mmm),41 Ca3Au7.16-7.43Ge3.84-3.57 (Imm2), and Ca3Au7.5-8.01Ge3.5-2.99 (Pnnm).27 The present YCd6-type derivatives Ca3Au14.3-14.5Ge4.7-4.5 (Im3) and Ca3.25Au12.5-12.9Ge5.5-5.1 (Im3) are new members. In addition, we have also found CaAu3Ge (Pa3)28 in this system (Table 1), which is isostructural with CaAu3Ga.24 Although both Ca3Au14.3-14.5Ge4.7-4.5 (I) and Ca3.25Au12.5-12.9Ge5.5-5.1 (II) may have larger phase widths, the compositions refined from representative single crystals are probably very close to respective phase boundaries according to the comparative lattice parameters given in Table 1. Accordingly, the 500 °C section of the partial phase diagram is shown in Figure 1 with the respective phase fields and the compositions studied (Table 1) marked. As can be seen, the phase widths of I (red) and II (blue) are very small, and their composition differences are only about 5-10 at %. However, they are clearly separated from each other. More demonstrations of the phase separation are given below in terms of lattice and atomic parameters, valence electrons, and so forth. Figure 2a shows the experimental powder pattern of the products from reaction 2, which lies between the subject, phases I and II. As seen, the experimental powder pattern is well fit by the patterns calculated from single crystal data sets 1 and 4 (with refined lattice constants of course), indicating the presence of a mixture of only I and II. Similar results are obtained according to the powder pattern of Yb15.3Au58.9Ge25.9 (reaction 15), Figure 2b. Fittings of the entire mixed patterns from reactions 3 and 13 are also shown in Supporting Information, Figure S1. All of these results indicate that I and II are equilibrium phases in the temperature range used, 400-500 °C. In addition, it should be noted that the two structural types, distinctive in their innermost disordered tetrahedron versus an isolated M atom, can also be easily distinguished according to the intensity of the (110) reflections.14 Supporting Information, Figure S2 shows this for the products of reactions 7 and 5, which are substantially pure I and II, respectively. The intensity of (110) peak (2θ = 8.4°) is only ∼1.4% of the strongest reflection ((543), 35.3°) (40) Merlo, F.; Pani, M.; Canepa, F.; Fornasini, M. L. J. Alloys Compd. 1998, 264, 82. (41) May, N.; Schaefer, H. Z. Naturforsch. 1972, 27b, 864.
Figure 2. Experimental (black) powder patterns of (a) Ca14.3Au62.5Ge23.1 and (b) Yb15.3Au58.9Ge25.9. Red and green curves are simulated using single crystal data for 1 and 4, and s3 and s4, respectively, together with their respective lattice constants (Table 1).
if a tetrahedron exists in the dodecahedron; on the contrary, it is ∼30% if a single atom is present. To our knowledge, paired products of spinodal decomposition42-44 also have the same symmetry and similar compositions, although a key factor for the occurrence of a spinodal decomposition is a negative second derivative of free energy with respect to composition.45 With this in mind, samples that produce mixtures of M3.25(Au,Ge)18 and M3(Au,Ge)19 (M = Ca, Yb) deserve further microscopic examinations because they may be occur as spinodal pairs, at least from the viewpoint of structure, symmetry, and composition. Crystal Structures. Actually, the shell geometries discussed below are common structural motifs for all YCd6type structures and their derivatives. Therefore, we will describe only the defect-free structure refined for crystal 1 (type II), which shows apparent complete chemical ordering between Au and Ge. Then the major structural differences among the other crystals studied will be pointed out. Figure 3 shows the multiply endohedral clusters in Ca3.25Au12.5Ge6.5 (1). The first shell, (a) a dodecahedron, is defined by 12 Ge5 and 8 Au3 atoms, with the latter on 3-fold axes. A single Ca atom lies at the cluster center, different from that in parent YCd6. The average center-tovertex distance for this shell is 3.61 A˚, ∼ 0.5 A˚ larger than other Ca-Au or Ca-Ge separations in the same structure. Thus Ca can be considered “rattling” in the dodecahedron, as also indicated by its larger displacement parameters (Table 3). Whether this “rattling” atom results in a good (42) Cahn, J. W. J. Chem. Phys. 1965, 42, 93. (43) Ditchek, B.; Schwartz, L. H. Annu. Rev. Mater. Sci. 1979, 9, 219. (44) Miyazaki, T. Process., Prop. Appl. Met. Ceram. Mater., Proc. Int. Conf. 1992, 1, 13. (45) Gibbs, J. W. Scientific Papers of J. Willard Gibbs; New York: Dover, 1961; Vol. 2, p 105, 252.
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Figure 3. Multiply endohedral polyhedral clusters in defect-free Ca3.25Au12.5Ge5.5 (Z = 2). (a) Ca8-centered Au8Ge12 dodecahedron, (b) Ca12 icosahedron, (c) Au30 icosidodecahedron, plus eight Au8 cubes (cyan, each consisting of 2 Au3 þ 6 Au1) centered by Ge7 (green), (d) Ge24E8 triacontahedron (E = empty vertex). Each of 60 triacontahedral edges is centered by an Au atom.
thermoelectric candidate as do Skutterudites46 or not is beyond this work. All pentagonal faces of the Au8Ge12 dodecahedron are outwardly capped by Ca9 atoms, which define a larger Ca12 icosahedron (b) as the second shell. This is the only shell in the structure completely defined by electropositive atoms. The center-to-vertex distance of this shell is 5.27 A˚, and the surface Ca9-Ca9 separations are about 5.55 A˚, meaning that they have no significant bonding to each other. Rather, they have strong interactions with the neighboring Au and Ge on pentagonal faces of both the inner dodecahedral and the next 30-atom icosidodecahedral shell (c). The last is defined by only Au atoms (24 Au1 þ 6 Au4), all in a sphere with average radii ∼5.90 A˚. The direct interactions among these Au atoms are not strong, as indicated by the intracluster distances dAu1-Au1 = 3.04 A˚ and dAu1-Au4 = 3.39 A˚. However, they have pronounced bonding interactions with Ge5 on the dodecahedral shell and Au1, Au2, and Ge6 atoms on the outmost triacontahedral shell (d), as indicated by the shorter intercluster separations, Au1-Ge5, 2.71 A˚; Au4-Ge5, 2.80 A˚; Au1-Au2, 2.87 A˚; Au1-Au3, 3.02 A˚; Au2-Au4, 2.95 A˚; and Au4-Au4, 2.93 A˚. The outermost triacontahedral shell consists of 32 vertices and 60 edges, with center-to-vertex distances in the range of 7.77-7.86 A˚. The decoration of the triacontahedral shell is noteworthy: of the 32 ideal vertices, the eight with real 3-fold symmetry are empty, and the others are unexceptionally occupied by Ge6 atoms. On the other hand, 60 Au atoms locate on all midedges of the triacontahedron. The interstitial Ge7 atoms always present at the Wyckoff 8c site (0.25, 0.25, 0.25) are alien to the parent YCd6.9 These are sandwiched between the icosidodecahedral and the triacontahedral shells, with strong bonding interactions with Au1 which is a member of both (dAu1-Ge7 = 2.62 A˚). Actually, each Ge7 also strongly interacts with Au3 atoms on the 3-fold axis of the dodecahedral shell, as indicated by the bond distance dAu3-Ge7 = 2.74 A˚. Thus each Ge7 is enclosed in an Au8 cube, as shown Figure 3c. The above structural motifs basically apply for all crystals studied in this work (2-5, s1-s4), except that (1) disordered tetrahedra of Au/Ge8 atoms occur within the dodecahedral shells in crystals 3-5, s2, and s4 (as in the parent YCd6), each atom at one-third occupancy; (2) (46) He, T.; Chen, J.; Rosenfeld, D. H.; Subramanian, M. A. Chem. Mater. 2006, 18, 759.
Figure 4. Plots of (a) lattice parameters and calculated volumes of dodecahedra, (b) refined Au occupancies at Au31 and Au/Ge5 sites, and (c) Au occupancies at Au/Ge8 site or Ca occupancies at Ca8 site as a function of valence electron counts per atom (e/a). The group of larger e/a values (left) pertain to type II crystals, Ca3.25(Au,Ge)18, the smaller e/a (right), to type I, Ca3(Au,Ge)19.
the 16f sites in all other crystals but 1 are split into two unequal components; (3) the sites equivalent to Ge5 (24g) in 1 are occupied by Au/Ge mixtures with increasing Au proportions; (4) both 48h and the site equivalent to Ge5 (24g) in 1 split into two parts in crystal s4, a special case. In summary, crystals 1, 2, s1, and s3 have same general formula of M3.25(Au,Ge)18 (II), whereas crystals 4, 5, s2, and s4, of M3(Au,Ge)19 (I), each with some small nonstoichiometry. Obviously, they are two different derivatives of YCd6. As for Ca3.05(2)Au13.69(8)Ge5.31(6) (3), the fact that it refined with both the customary disordered
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Figure 5. 3-D Fourier maps of electron densities around the origin in crystals: (a) 1, (b) 2, (c) 3, (d) 4, and (e), 5, respectively. Representative Wyckoff positions are labeled, and the minor split densities around 16f sites are marked with red arrows. The cutoff contour level is 14.0 e/A˚3. (The blue shadings represent core densities in the forward facing sections.).
tetrahedron and a fractional Ca (∼ 22(7)%) within the dodecahedron likely means it is a weakly modulated or intergrown crystal of both Ca3.25(Au,Ge)18 and Ca3(Au, Ge)19. The data set’s large intensity averaging factor (Rint = 0.193) probably relates to this effect (Table 2). However, co-refinement of both a tetrahedron and a single atom within dodecahedron is not new; rather, it was first reported for YbZn5.86 and Yb(Zn,Al)5.75.23 Nevertheless, we believe that crystal 3 is an intermediate state between Ca3.25(Au, Ge)18 and Ca3(Au,Ge)19, as supported by the following. Systematic Structural Changes. The seven Ca-based crystal structures (1-5, s1, and s2) provide useful clues regarding the evolution of different structural parameters as a function of the overall valence electron count per atom (e/a, assuming 1 e for Au). As shown in Figure 4a, the lattice parameters generally increase as e/a decreases, consistent with the increase in Au and decrease in Ge proportions in corresponding formulas (Table 2). As we know, Ge is smaller and electron richer and Au is larger in size and electron poorer. However, small cusps or inflections appear in all of the data over an e/a range of 1.86 and 1.79, in contrast to the smooth changes before (1 f s1 f 2) and afterward ( 4 f s2 f 5). These indicate that a phase or other transition may occur between 2 and 4. Actually, single crystal X-ray results support this conclusion because crystals 1, s1, and 2 belong to the Ca3.25(Au,Ge)18 structure II stoichiometrically whereas 4, s2, and 5, to the Ca3(Au,Ge)19 structure I. The occurrence of a presumably first-order phase transition is also supported by the volume changes for the dodecahedron (Figure 4a), the discontinuous Au occupancies at Au31 and Au/Ge5 (Figure 4b) sites, and the Au (or Ca) occupancies at Au/Ge8 (or Ca8) sites (Figure 4c), which exhibit either upward or downward inflections at the same e/a region, ∼1.86 or below. Figure 4 also reveals that the formation of crystals in the Ca3.25(Au,Ge)18 versus the Ca3(Au,Ge)19 family show strong correlations between lattice parameters and e/a values. The Ca3.25(Au,Ge)18 phase exists only in a region
with e/a g 1.86 and a < ∼14.72 A˚ under our synthetic conditions, whereas Ca3(Au,Ge)19 forms in a region with e/a e 1.79 and a > ∼14.80 A˚ (Figure 4a). In addition, these plots give clues about disorder and atomic decorations in both families. For example, the Au occupancy at the Au31 site (the major split part) tends to decrease from 1 to 5 (Figure 4b), in contrast, opposite changes are found for Au at Au/Ge5 and Au/Ge8 sites (Figures 4b and 4c). We will discuss the split phenomenon in more detail in the following section. Disorder within the Dodecahedra. From Table 3 and Supporting Information, Table S2, we know that the following types of disorder are observed among the present phases: an atom splitting at the 16f Au3 site, an occupancy disorder/mixing at Au/Ge5 and Au/Ge8 sites, and an orientational disorder at the Au/Ge8 site. All of these occur within the dodecahedral shell. Figure 5a-5e show the observed electron densities about and within this shell for crystals 1-5, respectively. As shown, the 16f Au3 sites split into two unequal parts for crystals 2-5. Close examination reveals an interesting image: for 2 and 3, small fractions (3-4%) refined outside of the dodecahedron (Figures 5b and 5c). On the contrary, small densities (8-10%) lie within the dodecahedron in 4 and 5 (Figures 5d and 5e). The relative positions of the split sites, the sizes of the dodecahedra, and their contents are correlated: small dodecahedral volumes, 660 A˚3. Electronic Structures. Figure 6 shows the densities-ofstates (DOS) of (a) Ca3.25Au12.5Ge5.5 (II, e/a = 1.93) and (b) Ca3Au12.5Ge6.5 (the model for I, e/a = 2.02). Basically, both patterns are quite similar although some core-like states between -10 eV and -8 eV split in (b). In both patterns, Au 5d populations lie within a range of -8 to -3 eV,
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Remarks
Figure 6. Calculated densities-of-states (DOS) of (a) Ca3.25Au12.5Ge5.5 (II) and (b) a Ca3Au12.5Ge6.5 model (I). The projected DOSs for Ca8 and Ge4 tetrahedra in the dodecahedra are shaded in orange at the bottom of the plots, respectively.
whereas s and p states of Au and Ge dominate below this. The Au/Ge s and p states also spread across the Fermi energy (EF). In contrast, the Ca 3d orbitals lie mainly above EF. The small contributions of Ca and of the Ge4 tetrahedron within the dodecahedral shell are represented by orange-shaded areas at the bottom of (a) and (b), respectively. The Ca states populate a high energy region (2-4 eV), with minor contributions at or below EF, whereas the Ge4 states spread thinly over a large energy range. In contrast to the DOS curves for “Ca3Au11.5In6.5”18 and “Ca3Au11Ga8”,19 which are bona fide ACs and exhibit pseudogaps at about EF, there is no apparent pseudogap for either of the present phases. This may explain our failure to find any Ca-Au-Ge quasicrystal.
Exploration of new YCd6-type quasicrystals and approximants continues to yield surprising results beyond imagination. This study also establishes that stable YCd6-type structures and derivatives continue to the east in the Periodic Table. Members of this family in different proportions span from binary Zn and Cd phases47 (with two valence electrons) to ternary triels18,19 (three electrons), and now to the tetrels (four electrons). How valence electrons and size are reconciled and how structures are regularized in this family are not a trivial matter. We have previously noticed that (a) stuffed YCd6-type structures can have 3:19 stoichiometries as well, for example, Ca3(Au,Ga)19,19 and (b) a large mismatch in atom sizes in these may result in the disappearance of the tetrahedron, as in YbZn5.8.23 However, the coexistence of both effects in our systems is a surprise. The discoveries of M3(Au,Ge)19 (I) and M3.25(Au,Ge)18 (II) (M = Ca, Yb) provide an unprecedented playground in which studies of important factors that govern phase formation and stability become possible, as discussed. These also raise the opportunity to probe some related and inspired “unknowns”, for example, the effect of “rattling” Ca within the dodecahedral shell versus thermoelectric properties, the possible occurrences of spinodal decompositions, and of modulation or intergrowth as well. The fact that both Ca3(Au,Ge)19 and Ca3.25(Au,Ge)18 exhibit the YCd6-type structural motif rather than Mg32(Al,Zn)49 type, as does Na 13Au20Ge 7.526 as well, is also striking. Finally, the discoveries of Ca3(Au,Ge)19 and Ca3.25(Au, Ge)18 open a new and exciting challenge: Does any QC exist in the presence of a corresponding AC that is isostructural with Ca3.25(Au,Ge)18, or even with nothing in the cluster center? Acknowledgment. This research was supported by the U.S. National Science Foundation, Solid State Chemistry, via Grants DMR-0444657 and -0853732. All of the work was performed in the facilities of the Ames Laboratory, U.S. Department of Energy. Supporting Information Available: Tables S1-S2, Figures S1-S2, and detailed CIF data. This material is available free of charge via the Internet at http://pubs.acs.org. (47) Villars, P.; Calvert, L. D. Pearson’s Handbook of Crystallographic Data for Intermetallic Phases, 2nd ed.; American Society of Metals: Materials Park, OH, 1991; Vol. 1.
